Relativistic Dynamics of Point Magnetic Moment

TL;DR

This paper develops a covariant framework for the dynamics of point particles with magnetic moments, exploring spin precession, force extensions, and their relation to electromagnetic theory and anomalies.

Contribution

It introduces a covariant formulation of magnetic forces and spin dynamics for point particles, connecting classical magnetic moment descriptions with relativistic symmetry.

Findings

Covariant spin precession lacks a unique form.

A covariant magnetic force formulation based on a magnetic 4-potential.

Discussion of the g-2 anomaly connection.

Abstract

The covariant motion of a classical point particle with magnetic moment in the presence of (external) electromagnetic fields is revisited. We are interested in understanding Lorentz force extension involving point particle magnetic moment (Stern-Gerlach force) and how the spin precession dynamics is modified for consistency. We introduce spin as a classical particle property inherent to Poincare\'e symmetry of space-time. We propose a covariant formulation of the magnetic force based on a \lq magnetic\rq\ 4-potential and show how the point particle magnetic moment relates to the Amperian (current loop) and Gilbertian (magnetic monopole) description. We show that covariant spin precession lacks a unique form and discuss connection to $g-2$ anomaly. We consider variational action principle and find that a consistent extension of Lorentz force to include magnetic spin force is not straightforward. We look at non-covariant particle dynamics, and present a short introduction to dynamics of (neutral) particles hit by a laser pulse of arbitrary shape.